Method and system for detecting whether an acoustic event has occured along a fluid conduit

ABSTRACT

Methods, systems, and techniques for determining whether an acoustic event lias occurred along a fluid conduit iliat lias acoustic sensors positioned along its length. For each of the sensors, a processor is used to determine a linear relationship between a measured acoustic signal measured using the sensor and a white noise acoustic source located along a longitudinal segment of the fluid conduit overlapping the sensor. From the linear relationship, the processor determines an acoustic path response that includes an acoustic response of the longitudinal segment and an acoustic source transfer function dial transforms the white noise acoustic source. Over time, variations in the acoustic path responses and/or acoustic source transfer functions are monitored. When the event threshold is exceeded, the acoustic event is identified as having occurred along the longitudinal segment corresponding to the acoustic path response or acoustic source transfer function that varied in excess of the event threshold.

TECHNICAL FIELD

The present disclosure is directed at methods, systems, and techniquesfor detecting whether an acoustic event has occurred along a fluidconduit such as a pipeline, well casing, or production tubing.

BACKGROUND

Pipelines and oil and gas wells are examples of conduits that are usedto transport liquids or gases (collectively, “fluids”) which, if leaked,could cause environmental damage. In the example of pipelines, the fluidmay comprise oil. In the example of an oil well, the fluid may compriseliquid production fluid or be gaseous, such as when casing vent flow orgas migration occurs. Accordingly, in certain circumstances it may bedesirable to monitor fluid conduits to determine whether a leak or otherevent potentially relevant to the integrity of the conduit has occurred.

SUMMARY

According to a first aspect, there is provided a method for determiningwhether an acoustic event has occurred along a fluid conduit havingacoustic sensors positioned therealong. The method comprisesdetermining, using a processor and for each of the sensors, a linearrelationship between a measured acoustic signal measured using thesensor and a white noise acoustic source located along a longitudinalsegment of the fluid conduit overlapping the sensor; and from the linearrelationship, an acoustic path response and an acoustic source transferfunction that transforms the white noise acoustic source. The methodfurther comprises monitoring over time variations in one or both of theacoustic path responses and acoustic source transfer functions;determining whether at least one of the variations exceeds an eventthreshold; and when at least one of the variations exceeds the eventthreshold, attributing the acoustic event to one of the sensorscorresponding to the acoustic path response or acoustic source transferfunction that varied in excess of the event threshold.

The processor may attribute the acoustic event to the one of the sensorsfor which the variation most exceeds the event threshold.

The acoustic event may comprise one of multiple acoustic events, andwherein the processor attributes one of the acoustic events to each ofthe sensors for which the variation exceeds the event threshold.

The acoustic path response may comprise an acoustic response of thelongitudinal segment and the acoustic event may be identified as havingoccurred along the longitudinal segment corresponding to the sensor towhich the acoustic event is attributed.

For each of the channels, the processor may determine the linearrelationship between the measured acoustic signal, the white noiseacoustic source located along the longitudinal segment, and white noiseacoustic sources located along any immediately adjacent longitudinalsegments.

Each element of the linear relationship may be a parameterized transferfunction that is parameterized using a finite impulse responsestructure.

The processor may determine the acoustic path responses and acousticsource transfer functions by factoring the linear relationship using alinear regression, wherein the linear regression may be factored into afirst array of parameterized transfer functions for determining theacoustic path responses and a second array of parameterized transferfunctions for determining the acoustic source transfer functions.

Each of the first and second arrays may be parameterized using a finiteimpulse response structure.

The method may further comprise, prior to monitoring variations in oneor both of the acoustic path responses and acoustic source transferfunctions, refining the one or both of the acoustic path responses andacoustic source transfer functions using weighted nullspace leastsquares.

The method may comprise determining a confidence bound for each of twoof the acoustic path responses or two of the acoustic source transferfunctions; from the confidence bounds, determining a statisticaldistance between the two of the acoustic source responses or the two ofthe acoustic source transfer functions; comparing the statisticaldistance to the event threshold; and identifying the acoustic event ashaving occurred when the statistical distance exceeds the eventthreshold.

The method may further comprising dividing the measured acoustic signalinto blocks of a certain duration prior to determining the linearrelationship.

Each of the longitudinal segments may be delineated by a pair of fiberBragg gratings located along an optical fiber and tuned to substantiallyidentical center wavelengths, and the method may further compriseoptically interrogating the optical fiber in order to obtain themeasured acoustic signal.

The optical fiber may extend parallel to the fluid conduit.

The optical fiber may be wrapped around the fluid conduit.

The optical fiber may be within a fiber conduit laid adjacent the fluidconduit.

The fluid conduit may comprise a pipeline.

According to another aspect, there is provided a system for detectingwhether an acoustic event has occurred along a fluid conduitlongitudinally divided into measurements channels. The system comprisesan optical fiber extending along the conduit and comprising fiber Bragggratings (FBGs), wherein each of the measurement channels is delineatedby a pair of the FBGs tuned to substantially identical centerwavelengths; an optical interrogator optically coupled to the opticalfiber and configured to optically interrogate the FBGs and to output anelectrical measured acoustic signal; and a signal processing unit. Thesignal processing unit comprises a processor communicatively coupled tothe optical interrogator; and a non-transitory computer readable mediumcommunicatively coupled to the processor, wherein the medium hascomputer program code stored thereon that is executable by the processorand that, when executed by the processor, causes the processor toperform the method of any of the foregoing aspects or suitablecombinations thereof.

The optical fiber may extends parallel to the fluid conduit.

The optical fiber may be wrapped around the fluid conduit.

The system may further comprise a fiber conduit adjacent the fluidconduit, wherein the optical fiber extends within the fiber conduit.

The fluid conduit may comprise a pipeline.

According to another aspect, there is provided a non-transitory computerreadable medium having stored thereon computer program code that isexecutable by a processor and that, when executed by the processor,causes the processor to perform the method of any of the foregoingaspects or suitable combinations thereof.

This summary does not necessarily describe the entire scope of allaspects. Other aspects, features and advantages will be apparent tothose of ordinary skill in the art upon review of the followingdescription of specific embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings, which illustrate one or more exampleembodiments:

FIG. 1A is a block diagram of a system for determining whether anacoustic event has occurred along a fluid conduit, which includes anoptical fiber with fiber Bragg gratings (“FBGs”) for reflecting a lightpulse, according to one example embodiment.

FIG. 1B is a schematic that depicts how the FBGs reflect a light pulse.

FIG. 1C is a schematic that depicts how a light pulse interacts withimpurities in an optical fiber that results in scattered laser light dueto Rayleigh scattering, which is used for distributed acoustic sensing(“DAS”).

FIG. 2 depicts a pipeline laying adjacent to a fiber conduit, accordingto one example embodiment.

FIGS. 3 and 4 depict block diagrams of a model for acoustic propagationalong a pipeline, according to additional example embodiments.

FIG. 5 depicts a test setup used to validate a method for determiningwhether an event has occurred along a fluid conduit, according toanother embodiment.

FIGS. 6-9 depict experimental results obtained using the test setup ofFIG. 5.

FIG. 10 depicts a method for determining whether an event has occurredalong a fluid conduit, according to another embodiment.

DETAILED DESCRIPTION

As used herein, “acoustics” refer generally to any type of “dynamicstrain” (strain that changes over time). Acoustics having a frequencybetween about 20 Hz and about 20 kHz are generally perceptible byhumans. Acoustics having a frequency of between about 5 Hz and about 20Hz are referred to by persons skilled in the art as “vibration”, andacoustics that change at a rate of <1 Hz, such as at 500 μHz, arereferred to as “sub-Hz strain”; as used herein, a reference to “about”or “approximately” a number or to being “substantially” equal to anumber means being within +/−10% of that number.

When using acoustics to determine whether an event, such as a pipelineleak, has occurred, it may be desirable to distinguish between differenttypes of events that generate different sounds, where “different” refersto a difference in one or both of acoustic intensity and frequency. Forexample, when the equipment being monitored is a buried oil pipeline, itmay be any one or more of a leak in that pipeline, a truck driving onthe land over that pipeline, and a pump operating near the pipeline thatare generating a sound. However, of the three events, it may only be theleak that requires immediate attention. Similarly, when monitoring awell, it may be one or both of pumping equipment and an instance ofcasing vent flow that generate a sound. Again, while the casing ventflow may require remediation, the standard operation of pumpingequipment does not.

The embodiments described herein are directed at methods, systems, andtechniques for detecting whether an acoustic event has occurred along afluid conduit such as a pipeline. Optical interferometry using fiberBragg gratings (“FBGs”), as described in further detail with respect toFIGS. 1A-1C, is used to measure acoustics. In some of the embodimentsdescribed herein, a processor determines a measured acoustic signalusing optical interferometry and from that measured acoustic signaldetermines whether a particular event, such as a pipeline leak, hasoccurred.

Referring now to FIG. 1A, there is shown one embodiment of a system 100for fiber optic sensing using optical fiber interferometry. The system100 comprises an optical fiber 112, an interrogator 106 opticallycoupled to the optical fiber 112, and a signal processing device(controller) 118 that is communicative with the interrogator 106. Whilenot shown in FIG. 1A, within the interrogator 106 are an optical source,optical receiver, and an optical circulator. The optical circulatordirects light pulses from the optical source to the optical fiber 112and directs light pulses received by the interrogator 106 from theoptical fiber 112 to the optical receiver.

The optical fiber 112 comprises one or more fiber optic strands, each ofwhich is made from quartz glass (amorphous SiO₂). The fiber opticstrands are doped with a rare earth compound (such as germanium,praseodymium, or erbium oxides) to alter their refractive indices,although in different embodiments the fiber optic strands may not bedoped. Single mode and multimode optical strands of fiber arecommercially available from, for example, Corning® Optical Fiber.Example optical fibers include ClearCurve™ fibers (bend insensitive),SMF28 series single mode fibers such as SMF-28 ULL fibers or SMF-28efibers, and InfiniCor® series multimode fibers.

The interrogator 106 generates sensing and reference pulses and outputsthe reference pulse after the sensing pulse. The pulses are transmittedalong optical fiber 112 that comprises a first pair of FBGs. The firstpair of FBGs comprises first and second FBGs 114 a,b (generally, “FBGs114”). The first and second FBGs 114 a,b are separated by a fiber opticsensor 116 that comprises a segment of fiber extending between the firstand second FBGs 114 a,b. The length of the sensor 116 varies in responseto an event (such as an acoustic event) that the optical fiber 112experiences. Each fiber segment between any pair of adjacent FBGs 114with substantially identical center wavelengths is referred to as a“sensor” 116 of the system 200. The system 200 accordingly comprisesmultiple sensors 116, each of which is a distributed sensor 116 thatspans the length of the segment between the adjacent FBGs 114. Anexample sensor length is 25 m. In the depicted embodiment, the FBGs 114are consistently separated by, and the sensors 116 accordingly each havea length of, 25 m; however, in different embodiments (not depicted) anyone or more of the sensors 116 may be of different lengths.

The light pulses have a wavelength identical or very close to the centerwavelength of the FBGs 114, which is the wavelength of light the FBGs114 are designed to partially reflect; for example, typical FBGs 114 aretuned to reflect light in the 1,000 to 2,000 nm wavelength range. Thesensing and reference pulses are accordingly each partially reflected bythe FBGs 114 a,b and return to the interrogator 106. The delay betweentransmission of the sensing and reference pulses is such that thereference pulse that reflects off the first FBG 114 a (hereinafter the“reflected reference pulse”) arrives at the optical receiver 103simultaneously with the sensing pulse that reflects off the second FBG114 b (hereinafter the “reflected sensing pulse”), which permits opticalinterference to occur.

While FIG. 1A shows only the one pair of FBGs 114 a,b, in differentembodiments (not depicted) any number of FBGs 114 may be on the fiber112, and time division multiplexing (“TDM”) (and optionally, wavelengthdivision multiplexing (“WDM”)) may be used to simultaneously obtainmeasurements from them. If two or more pairs of FBGs 114 are used, anyone of the pairs may be tuned to reflect a different center wavelengththan any other of the pairs. Alternatively a group of multiple FBGs 114may be tuned to reflect a different center wavelength to another groupof multiple FBGs 114 and there may be any number of groups of multipleFBGs extending along the optical fiber 112 with each group of FBGs 114tuned to reflect a different center wavelength. In these exampleembodiments where different pairs or group of FBGs 114 are tuned toreflect different center wavelengths to other pairs or groups of FBGs114, WDM may be used in order to transmit and to receive light from thedifferent pairs or groups of FBGs 114, effectively extending the numberof FBG pairs or groups that can be used in series along the opticalfiber 112 by reducing the effect of optical loss that otherwise wouldhave resulted from light reflecting from the FBGs 114 located on thefiber 112 nearer to the optical source 101. When different pairs of theFBGs 114 are not tuned to different center wavelengths, TDM issufficient.

The interrogator 106 emits laser light with a wavelength selected to beidentical or sufficiently near the center wavelength of the FBGs 114that each of the FBGs 114 partially reflects the light back towards theinterrogator 106. The timing of the successively transmitted lightpulses is such that the light pulses reflected by the first and secondFBGs 114 a,b interfere with each other at the interrogator 106, and theoptical receiver 103 records the resulting interference signal. Theevent that the sensor 116 experiences alters the optical path lengthbetween the two FBGs 114 and thus causes a phase difference to arisebetween the two interfering pulses. The resultant optical power at theoptical receiver 103 can be used to determine this phase difference.Consequently, the interference signal that the interrogator 106 receivesvaries with the event the sensor 116 is experiencing, which allows theinterrogator 106 to estimate the magnitude of the event the sensor 116experiences from the received optical power. The interrogator 106digitizes the phase difference and outputs an electrical signal (“outputsignal”) whose magnitude and frequency vary directly with the magnitudeand frequency of the event the sensor 116 experiences.

The signal processing device (controller) 118 is communicatively coupledto the interrogator 106 to receive the output signal. The signalprocessing device 118 includes a processor 102 and a non-transitorycomputer readable medium 104 that are communicatively coupled to eachother. An input device 110 and a display 108 interact with the processor102. The computer readable medium 104 has encoded on it computer programcode to cause the processor 102 to perform any suitable signalprocessing methods to the output signal. For example, if the sensor 116is laid adjacent a region of interest that is simultaneouslyexperiencing acoustics from two different sources, one at a rate under20 Hz and one at a rate over 20 Hz, the sensor 116 will experiencesimilar strain and the output signal will comprise a superposition ofsignals representative of those two sources. The processor 102 may applya low pass filter with a cutoff frequency of 20 Hz to the output signalto isolate the lower frequency portion of the output signal from thehigher frequency portion of the output signal. Analogously, to isolatethe higher frequency portion of the output signal from the lowerfrequency portion, the processor 102 may apply a high pass filter with acutoff frequency of 20 Hz. The processor 102 may also apply more complexsignal processing methods to the output signal; example methods includethose described in PCT application PCT/CA2012/000018 (publication numberWO 2013/102252), the entirety of which is hereby incorporated byreference.

FIG. 1B depicts how the FBGs 114 reflect the light pulse, according toanother embodiment in which the optical fiber 112 comprises a third FBG114 c. In FIG. 1B, the second FBG 114 b is equidistant from each of thefirst and third FBGs 114 a,c when the fiber 112 is not strained. Thelight pulse is propagating along the fiber 112 and encounters threedifferent FBGs 114, with each of the FBGs 114 reflecting a portion 115of the pulse back towards the interrogator 106. In embodimentscomprising three or more FBGs 114, the portions of the sensing andreference pulses not reflected by the first and second FBGs 114 a,b canreflect off the third FBG 114 c and any subsequent FBGs 114, resultingin interferometry that can be used to detect an event along the fiber112 occurring further from the optical source 101 than the second FBG114 b. For example, in the embodiment of FIG. 1B, a portion of thesensing pulse not reflected by the first and second FBGs 114 a,b canreflect off the third FBG 114 c and a portion of the reference pulse notreflected by the first FBG 114 a can reflect off the second FBG 114 b,and these reflected pulses can interfere with each other at theinterrogator 106.

Any changes to the optical path length of the sensor 116 result in acorresponding phase difference between the reflected reference andsensing pulses at the interrogator 106. Since the two reflected pulsesare received as one combined interference pulse, the phase differencebetween them is embedded in the combined signal. This phase informationcan be extracted using proper signal processing techniques, such asphase demodulation. The relationship between the optical path of thesensor 116 and that phase difference (θ) is

${\theta = \frac{2\pi \; {nL}}{\lambda}},$

where n is the index of refraction of the optical fiber; L is theoptical path length of the sensor 116; and λ is the wavelength of theoptical pulses. A change in nL is caused by the fiber experiencinglongitudinal strain induced by energy being transferred into the fiber.The source of this energy may be, for example, an object outside of thefiber experiencing the acoustics.

One conventional way of determining ΔnL is by using what is broadlyreferred to as distributed acoustic sensing (“DAS”). DAS involves layingthe fiber 112 through or near a region of interest and then sending acoherent laser pulse along the fiber 112. As shown in FIG. 1C, the laserpulse interacts with impurities 113 in the fiber 112, which results inscattered laser light 117 because of Rayleigh scattering. Vibration oracoustics emanating from the region of interest results in a certainlength of the fiber becoming strained, and the optical path change alongthat length varies directly with the magnitude of that strain. Some ofthe scattered laser light 117 is back scattered along the fiber 112 andis directed towards the optical receiver 103, and depending on theamount of time required for the scattered light 117 to reach thereceiver and the phase of the scattered light 117 as determined at thereceiver, the location and magnitude of the vibration or acoustics canbe estimated with respect to time. DAS relies on interferometry usingthe reflected light to estimate the strain the fiber experiences. Theamount of light that is reflected is relatively low because it is asubset of the scattered light 117. Consequently, and as evidenced bycomparing FIGS. 1B and 1C, Rayleigh scattering transmits less light backtowards the optical receiver 103 than using the FBGs 114.

DAS accordingly uses Rayleigh scattering to estimate the magnitude, withrespect to time, of the event experienced by the fiber during aninterrogation time window, which is a proxy for the magnitude of theevent, such as vibration or acoustics emanating from the region ofinterest. In contrast, the embodiments described herein measure eventsexperienced by the fiber 112 using interferometry resulting from laserlight reflected by FBGs 114 that are added to the fiber 112 and that aredesigned to reflect significantly more of the light than is reflected asa result of Rayleigh scattering. This contrasts with an alternative useof FBGs 114 in which the center wavelengths of the FBGs 114 aremonitored to detect any changes that may result to it in response tostrain. In the depicted embodiments, groups of the FBGs 114 are locatedalong the fiber 112. A typical FBG can have a reflectivity rating of 2%or 5%. The use of FBG-based interferometry to measure interferencecausing events offers several advantages over DAS, in terms of opticalperformance.

FIGS. 2-10 depict embodiments of methods, systems, and techniques fordetermining whether an acoustic event has occurred along a fluidconduit, such as a wellbore (e.g., well casing, production tubing) orpipeline. In certain embodiments, the system 100 of FIG. 1A obtains ameasured acoustic signal using the sensors 116 placed along a pipelineto estimate the acoustic response of the path along which the acousticsignal propagates (hereinafter interchangeably referred to as the“acoustic path response”), which comprises the response of the fluidconduit, and the frequency content of external signals affecting thepipeline, which are modeled as acoustic source transfer functions thattransform white noise acoustic sources. Being able to distinguishbetween changes in the acoustic path response and changes in thefrequency content of the external signals affecting the pipeline may beused in leak detection and pipeline monitoring systems.

Technical challenges when developing a leak detection system comprise:

-   1. enabling real-time reporting of leaks;-   2. the ability to sense small leaks;-   3. automatically detecting leaks irrespective of environmental and    operating conditions;-   4. accurately estimating leak location; and-   5. avoiding false alarms, which may comprise identifying and    categorizing events other than leaks.

Certain embodiments described herein are able to continuously monitorpipelines using acoustic sensing equipment. FIG. 2 shows an examplesystem 200 comprising a fluid conduit in the form of a pipeline 204 laidalongside a fiber conduit 202 within which is the optical fiber 112. Apair of acoustic events 208 a,b (generally, “acoustic events 208”) aredepicted. The acoustic event 208 b on the pipeline 204 may represent,for example, a leak. As discussed above in respect of FIGS. 1A-1C, theFBGs 114 are sensitive to acoustics of various frequencies. The FBGs 114accordingly comprise the functionality of a microphone andaccelerometer. The conduit 202 is placed on or sufficiently near thepipeline 204 so as to be able to measure acoustics generated by theacoustic events 208. In certain example embodiments, the conduit 202contacts the pipeline 204 or is within 10 cm, 20 cm, 30 cm, 40 cm, 50cm, 60 cm, 70 cm, 80 cm, 90 cm, 1 m, 2 m, 3 m, 4 m, or 5 m of thepipeline 204. The FBGs 114 in the depicted embodiment are etched intothe fiber 112 at 25 m intervals. Three sensors 116 a-c are accordinglydepicted in FIG. 2, although in different embodiments (not depicted)there may be as few as two of the sensors 116 or many more than three ofthe sensors 116.

Each of the sensors 116 a-c in the depicted embodiment overlaps with alongitudinal segment of the pipeline 204, with none of the longitudinalsegments overlapping each other and all of the longitudinal segmentscollectively forming a continuous portion of the pipeline 204. Indifferent embodiments (not depicted), the longitudinal segments of thepipeline 204 that are monitored may not be continuous. For example, anytwo or more neighbouring longitudinal segments may be spaced apart solong as the neighbouring segments remain acoustically coupled to eachother. Additionally or alternatively, in different embodiments (notdepicted) the fiber 112 may not extend parallel with the pipeline 204.For example, in one example the fiber 112 is wound around segments ofthe pipeline 204 to increase sensitivity.

The system 200 of FIG. 2 permits continuous measurements to be obtainedusing the FBGs 114, thus facilitating real-time reporting of leaks. Asdifferent sensors correspond to different longitudinal segments of thepipeline 204, event localization becomes easier. Also, using the conduit202, which may be plastic, to house the optical fiber 112 permitsrelatively straightforward installation. As discussed in more detailbelow, certain embodiments described herein are able to sense relativelysmall leaks and leaks occurring under low pipeline pressure or slackconditions.

Many conventional event detection systems are able to detect events 208,such as leaks or flow rate changes, when they have a priori knowledgeabout when the event is expected to occur. A more technicallychallenging problem is performing event detection without that a prioriinformation. Similarly, many conventional event detection systems areable to detect events 208 during periods of relatively constantenvironmental or ambient conditions. A more technically challengingproblem is performing event detection when one or both of operating andenvironmental conditions are changing.

At least some of the embodiments described herein address thesetechnical challenges. The processor 102 extracts leak relevant featuresfrom the measured acoustic signal. Fluid escaping from the pipeline 204may do any one or more of:

-   1. emit a broadband sound (a hiss);-   2. cause a vibration along the pipeline 204;-   3. cause a strain on the conduit 202 (as fluid escaping the pipeline    204 hits the conduit 202);-   4. decrease pressure in the pipeline 204; and-   5. related to any pressure decrease, cause a decrease in mass flow    rate in the pipeline 204 downstream of the leak.

Whenever a leak is present, a hole or crack in the pipeline 204 is alsopresent. The leak itself may have different causes including any one ormore of:

-   1. denting or buckling in the pipeline 204;-   2. a faulty seal between two flanges comprising the pipeline 204    (e.g., if the flanges are not bolted sufficiently tightly together);-   3. corrosion in the pipeline 204;-   4. movement of the ground surrounding the pipeline 204; and-   5. an intrusion attempt or accidental damage of the pipeline 204    using machinery.

The processor 102 distinguishes the aforementioned causes of the leakfrom normal or non-critical events affecting the pipeline 204, such as:

-   1. changes in fluid flow rate;-   2. changes in fluid density;-   3. external environmental sounds due to traffic, rivers, wind, rain,    etc.;-   4. changes in soil composition due to rain;-   5. changes in the pipeline 204, FBGs 114, or material surrounding    the pipeline 204 due to daily temperature cycles;-   6. vibrations due to machinery such as pumps and compressors    attached to or near the pipeline 204; and-   7. sensor errors and temporary sensor failures, etc.

Described herein is an approach to estimate both the acoustic pathresponse, which in certain embodiments comprises the pipeline's 204frequency response, and the frequency content of acoustic sourcesaffecting the pipeline 204. By obtaining estimates of (and monitoring)both the pipeline's 204 frequency response and the acoustic sources'frequency content the processor 102 determines at least some of thefeatures and causes of leaks listed above. For example:

-   1. A dent or buckling of the pipeline 204 changes the frequency    response of the longitudinal segment of the pipeline 204 comprising    that dent or buckling.-   2. Changing the pressure of the fluid in the pipeline 204 causes    changes in both the acoustic path response and the frequency content    of an acoustic source. The change in the acoustic path response does    not result from a change in the response of the pipeline 204 per se,    but the pressure of the fluid flowing through the pipeline 204.    Thus, by monitoring for these changes the processor 102 in certain    embodiments estimates the fluid pressure for each of the pipeline's    204 longitudinal segments. Once an estimate of the pressure for each    of the segments is obtained, in certain embodiments the processor    102 detects leaks by monitoring for drops in pressure along    downstream segments.-   3. If the frequency content of an acoustic source affecting a    particular longitudinal segment suddenly exhibits an increase in    broadband content, this may be due to the “hiss” of a leak in that    segment.

The processor 102, by being sensitive to several features of a leak,increases sensitivity to leaks and reduces the likelihood of a falsepositive occurring. The more features that are detected that areconsistent with a leak, the more confidence associated with theprocessor's 102 determination that a leak is present.

The following assumptions apply to the pipeline 204 and system 200 ofFIG. 2:

-   1. An event 208 acts as an acoustic source. Acoustic sources may    also comprise, for example, environmental noise or sound emitted by    a leak.-   2. An acoustic source “is attributed to” one of the sensors 116 when    the acoustics that that source emits are first detected by that one    of the sensors 116. In an embodiment in which the pipeline 204    extends substantially parallel to the ground, an acoustic source    accordingly is attributed to one of the sensors 116 when a line from    that acoustic source extending to the longitudinal segment of the    pipeline 204 monitored by that one of the sensors 116 is    perpendicular to that pipeline 204 segment. As discussed in further    detail below, all acoustic sources, whether they comprise events 208    or other acoustic generators, such as environmental noise or sound    emitted by a leak, attributed to one of the sensors 116 are summed    into a single acoustic source for that one of the sensors 116.-   3. The acoustic sources occur in, on, or near the pipeline 204. An    acoustic source is “near” a pipeline when the acoustics emitted by    the source are measurable by at least one of the sensors 116.-   4. Acoustic sources are mutually uncorrelated.-   5. Acoustic waves travel along an acoustic path that extends through    various media including the fluid in the pipeline 204, the pipeline    204 wall, and material surrounding the pipeline 204.-   6. Acoustic waves are reflected by valves, imperfections, etc. in    the pipeline 204, and interfaces in the material surrounding the    pipeline 204.-   7. Leaks are not always present, but when they occur they resemble a    broadband stochastic process.

A measured acoustic signal is a measurement of an acoustic signalresulting from a superposition of signals from multiple acoustic sources(each a “source signal”) that reach the sensor 116 via multiple paths;those acoustic sources may represent acoustic events 208, other sources,or both. Thus when an acoustic event 208 occurs along the pipeline 204,the processor 104 detects the event 208 using several of the nearestsensors 116 as the source signal generated by the event 208 propagatesthrough the ground, pipeline 204 wall, and fluid inside the pipeline204. Consequently, even though an event 208 is only attributed to one ofthe sensors 116, many of the sensors 116 are able to measure the event208. Two features that distinguish a measured acoustic signal from thesource signals that cause it are:

-   1. a single source signal generated by a single acoustic source near    the pipeline 204 is present in many of the measured acoustic signals    measured along different sensors 116; and-   2. a measured acoustic signal may separately comprise a source    signal and its reflection, which is treated as another source    signal. A source signal per se excludes its reflections.

As source signals travel through a medium to reach one or more of thesensors 112 (possibly along many different paths), they are affected bythe medium through which they are travelling. Thus the measured acousticsignal is a sum of filtered versions of one or more source signalsemanating from one or more acoustic sources. For any given one of thesensors 116, the transfer function describing the filtering of thesource signal generated by the acoustic source as it propagates to thatone of the sensors 116 is called the “path response” and in embodimentsin which the pipeline 204 is being monitored for leaks comprises theacoustic response of the longitudinal segment of the pipeline 204corresponding to that one of the sensors 116.

Acoustics Propagation Model

FIG. 3 depicts a block diagram of a model 300 for acoustic wavepropagation along the pipeline 204 in which the pipeline 204 is deemedto be extending in the left and right directions for convenience. Themodel 300 is not “identifiable” in that given proper data, estimates ofall the desired transfer functions used in the model 300 cannot bedetermined. In FIG. 3 the model's 300 nodes and blocks are defined asfollows:

-   1. w_(i) ^(λ) denotes an acoustic wave at sensor 116 i propagating    to the left;-   2. w_(i) ^(r) denotes an acoustic wave at sensor 116 i propagating    to the right;-   3. G₁₂ ^(i) denotes the path response of an acoustic wave    propagating to the left from sensor 116 i+1 to i;-   4. G₂₁ ^(i) denotes the path response of an acoustic wave    propagating to the right from sensor 116 i to i+1;-   5. G₁₁ ^(i) denotes the path response of an acoustic wave that was    traveling to the right at sensor 116 i, and was reflected (i.e. is    now traveling to the left) before it reached sensor 116 i+1;-   6. G₂₂ ^(i) denotes the path response of an acoustic wave that was    traveling to the left at sensor i+1 and was reflected before it    reached sensor 116 i;-   7. e_(i) denotes an acoustic source that is attributed to in sensor    116 i. Sources are represented as white stochastic processes (white    noise) and are hereinafter interchangeably referred to as “external    signals” e_(i);-   8. H_(r) ^(i) denotes the frequency content of the source signal    originating from source e_(i) traveling to the right. It is assumed    that the source signal generated by source i predominantly follows    the path of the other acoustic waves traveling to the right; and-   9. H₈₀ ^(i) denotes the frequency content of the source signal    originating from source e_(i) traveling to the left. It is assumed    that the source signal generated by source i predominantly follows    the path of the other acoustic waves traveling to the left.

In FIG. 3, the acoustic path response for one of the sensors 116 i ischaracterized by G₁₂ ^(i), G₂₁ ^(i), G₁₁ ^(i), and G₂₂ ^(i).

An acoustic measurement at sensor 116 i at time t is modeled as:

w _(i)(t)=F _(i)(q) (w_(i) ^(r)(t)+

(t))+s _(i)(t)   (1)

where F_(i) is the acoustic sensor frequency response, and s, is sensornoise (i.e. measurement error). The sensor 116 measures acoustic wavestraveling in both directions. Unless otherwise stated herein, s isassumed to be very small compared to e_(i) and accordingly can forpractical purposes be dropped from the equations. A component of thesensor frequency response is an integration over the sensor's 116length.

The transfer functions G₁₂ ^(i), G₂₁ ^(i), G₁₁ ^(i), and G₂₂ ^(i)describe the acoustic path response; that is, the acoustic response ofthe path the acoustic wave travels, which in the depicted embodimentcomprises the pipeline 204. Thus these transfer functions are affectedby physical changes in the pipeline 204 due to dents, corrosion, fluiddensity, fluid flow rate, fluid pressure within the pipeline 204,material surrounding the pipeline 204, and the like. On the other hand,the transfer functions H_(r) ^(i) and H_(λ) ^(i) describe the filterthat shapes the source signals affecting the pipeline 204 as generatedby the external sources e_(i). As discussed above, those acoustic wavesare by definition white noise, and so the filter H_(r) ^(i) changesaccording to the frequency content of the external sources e_(i)affecting the pipeline 204 such as wind, machinery, traffic noise, rivernoise, etc.

Given the measurements w_(i), i=1,2,K the transfer functions G₁₂ ^(i),G₂₁ ^(i), G₁₁ ^(i), G₂₂ ^(i), H_(r) ^(i), and H₈₀ ^(i) i=1,2,K in themodel 300 shown in FIG. 3 are not identifiable primarily due to the factthat the measured acoustic signal is a superposition of acoustic waves(filtered source signals) travelling in all directions.

The mathematical relationship between the measured variables w_(i),i=1,2,K is determined below. A mathematical representation of theequations illustrated in FIG. 3 for a six sensor setup is:

$\begin{matrix}{\quad{\begin{bmatrix}\omega_{1}^{} \\\omega_{1}^{r} \\\omega_{2}^{} \\\omega_{2}^{r} \\\omega_{3}^{} \\\omega_{3}^{r} \\\omega_{4}^{} \\\omega_{4}^{r} \\\omega_{5}^{} \\\omega_{5}^{r} \\\omega_{6}^{} \\\omega_{6}^{r}\end{bmatrix} = {\quad{\quad{\left\lbrack \begin{matrix}\; & G_{11}^{1} & G_{12}^{1} & \; & \; & \; & \; & \; & \; & \; & \; & \; \\G_{22}^{0} & \; & \; & \; & \; & \; & \; & \; & \; & \; & \; & \; \\\; & \; & \; & G_{11}^{2} & G_{12}^{2} & \; & \; & \; & \; & \; & \; & \; \\\; & G_{21}^{1} & G_{22}^{1} & \; & \; & \; & \; & \; & \; & \; & \; & \; \\\; & \; & \; & \; & \; & G_{11}^{3} & G_{12}^{3} & \; & \; & \; & \; & \; \\\; & \; & \; & G_{21}^{2} & G_{22}^{2} & \; & \; & \; & \; & \; & \; & \; \\\; & \; & \; & \; & \; & \; & \; & G_{11}^{4} & G_{11}^{4} & \; & \; & \; \\\; & \; & \; & \; & \; & G_{21}^{3} & G_{21}^{3} & \; & \; & \; & \; & \; \\\; & \; & \; & \; & \; & \; & \; & \; & \; & G_{11}^{5} & G_{12}^{5} & \; \\\; & \; & \; & \; & \; & \; & \; & G_{21}^{4} & G_{22}^{4} & \; & \; & \; \\\; & \; & \; & \; & \; & \; & \; & \; & \; & \; & \; & G_{11}^{6} \\\; & \; & \; & \; & \; & \; & \; & \; & \; & G_{21}^{5} & G_{22}^{5} & \;\end{matrix} \right\rbrack {\quad{\begin{bmatrix}\omega_{1}^{} \\\omega_{1}^{r} \\\omega_{2}^{} \\\omega_{2}^{r} \\\omega_{3}^{} \\\omega_{3}^{r} \\\omega_{4}^{} \\\omega_{4}^{r} \\\omega_{5}^{} \\\omega_{5}^{r} \\\omega_{6}^{} \\\omega_{6}^{r}\end{bmatrix} + {{\begin{bmatrix}\; & H_{\lambda}^{1} & \; & \; & \; & \; & \; & \; \\H_{r}^{0} & H_{r}^{1} & \; & \; & \; & \; & \; & \; \\\; & \; & H_{\lambda}^{2} & \; & \; & \; & \; & \; \\\; & \; & H_{r}^{2} & \; & \; & \; & \; & \; \\\; & \; & \; & H_{\lambda}^{3} & \; & \; & \; & \; \\\; & \; & \; & H_{r}^{3} & \; & \; & \; & \; \\\; & \; & \; & \; & H_{\lambda}^{4} & \; & \; & \; \\\; & \; & \; & \; & H_{r}^{4} & \; & \; & \; \\\; & \; & \; & \; & \; & H_{\lambda}^{5} & \; & \; \\\; & \; & \; & \; & \; & H_{r}^{5} & \; & \; \\\; & \; & \; & \; & \; & \; & H_{\lambda}^{6} & H_{\lambda}^{7} \\\; & \; & \; & \; & \; & \; & H_{r}^{6} & \;\end{bmatrix}\begin{bmatrix}e_{0} \\\begin{matrix}e_{1} \\e_{2} \\e_{3} \\e_{4} \\e_{5} \\e_{6} \\e_{7}\end{matrix}\end{bmatrix}}.}}}}}}}} & (2)\end{matrix}$

Equation (2) can be expressed as:

w ^(m)(t)=G ^(m)(q)w ^(m)(t)+H ^(m)(q)e ^(m)(t)   (3)

An equation in terms of w_(i)'s as defined in Equation (1) is desirable.The expression for w^(m) in terms of only e^(m) is

w ^(m)=(I−G ^(m))⁻¹ H ^(m) e ^(m)   (4)

where the inverse is guaranteed to exist because I−G^(m) is monic. Inorder to obtain an expression with a vector of F_(i)(q)(w_(i) ^(r)+w_(i)^(λ)), i=1,2,K, on the left hand side, premultiply Equation (4) by

$M = \begin{bmatrix}F_{1} & F_{1} & \; & \; & \; & \; & \; & \; & \; & \; & \; & \; \\\; & \; & F_{2} & F_{2} & \; & \; & \; & \; & \; & \; & \; & \; \\\; & \; & \; & \; & F_{3} & F_{3} & \; & \; & \; & \; & \; & \; \\\; & \; & \; & \; & \; & \; & F_{4} & F_{4} & \; & \; & \; & \; \\\; & \; & \; & \; & \; & \; & \; & \; & F_{5} & F_{5} & \; & \; \\\; & \; & \; & \; & \; & \; & \; & \; & \; & \; & F_{6} & F_{6}\end{bmatrix}$

resulting in

w(t)=M(q)(I−G ^(m)(q))⁻¹ H ^(m)(q)e(t)=W(q)e(t)   (5)

where the elements of w are w_(i) as defined in Equation (1) andw(q)=M(q)(I−G^(m)(q))⁻¹H^(m)(q). Two points about Equation (5) are:

-   1. The matrix W is a full matrix (i.e. all entries are non-zero). In    particular, each entry is a product of H_(r) ^(i), H_(λ) ^(i), and    G_(mn) ^(i), m,n=1,2, and i=1,2,3,K.-   2. Due to the structure of the network shown in FIG. 3, W can be    factored into two matrices of transfer functions, where one of the    matrices of transfer functions depends only on the acoustic path    responses G₁₁ ^(i), G₁₂ ^(i), G₂₁ ^(i), i=1,2,K.

Determining the acoustic path responses the pipeline 204 segments beingmonitored by the sensors 116 is desired. Because each element in W is afunction of G₁₁ ^(i), G₁₂ ^(i), G₂₁ ^(i), G₂₂ ^(i), H_(r) ^(i)'s and H₈₀^(i), i=1,2,K it is not sufficient to monitor the transfer functions ofW. In order to independently monitor the acoustic path responses fromthe acoustic sources e, affecting the pipeline, W is factored. W can befactored as:

W(q)=F(q) (I−G(q))⁻¹ H(q)   (6)

where F=diag(F₁, K, F₆), and

$\; {{G = \begin{bmatrix}0 & G_{12} & \; & \; & \; & \; \\G_{21} & 0 & G_{23} & \; & \; & \; \\\; & G_{32} & 0 & G_{34} & \; & \; \\\; & \; & G_{43} & 0 & G_{45} & \; \\\; & \; & \; & G_{54} & 0 & G_{56} \\\; & \; & \; & \; & G_{65} & 0\end{bmatrix}},{H = \begin{bmatrix}H_{10} & H_{1} & H_{12} & \; & \; & \; & \; & \; \\\; & H_{21} & H_{2} & H_{23} & \; & \; & \; & \; \\\; & \; & H_{32} & H_{3} & H_{34} & \; & \; & \; \\\; & \; & \; & H_{43} & H_{4} & H_{45} & \; & \; \\\; & \; & \; & \; & H_{54} & H_{5} & H_{56} & \; \\\; & \; & \; & \; & \; & H_{65} & H_{6} & H_{67}\end{bmatrix}},}$

where

${G_{ij} = {{\frac{G_{12}^{i}N_{i - 1}}{D_{{i - 1},i}}\mspace{14mu} {if}\mspace{11mu} i} < j}},{G_{ij} = {{\frac{G_{21}^{j}}{D_{{i - 1},i}}\mspace{14mu} {if}\mspace{11mu} i} < j}},{H_{i} = \frac{{{H_{}^{i}\left( {1 + G_{22}^{i}} \right)}N_{i - 1}} + {{H_{r}^{i}\left( {1 + G_{11}^{i - 1}} \right)}N_{i}}}{D_{{i - 1},i}}},{H_{ij} = {{- G_{ij}}H_{p}^{i}}},{{{if}\mspace{11mu} i} < j},{H_{ij} = {{- G_{ij}}H_{}^{i}}},{{{if}\mspace{11mu} i} < j},$

where

${N_{k} = {\det \begin{bmatrix}{1 + G_{11}^{k}} & G_{12}^{k} \\G_{21}^{k} & {1 + G_{22}^{k}}\end{bmatrix}}},{D_{mn} = {{\det \begin{bmatrix}{1 + G_{11}^{m}} & G_{12}^{m} & \; & \; \\\; & 1 & G_{11}^{n} & G_{12}^{n} \\G_{21}^{m} & G_{22}^{m} & 1 & \; \\\; & \; & G_{21}^{n} & {1 + G_{22}^{n}}\end{bmatrix}}.}}$

Using the factorization of Equation (6), a network equation relating themeasured variables is:

w(t)=W(q)e(t)

F ⁻¹(q)w(t)=G(q)F ⁻¹(q)w(t)+H(q)e(t)

w(t)=F(q)G(q)F ⁻¹(q)w(t)+F(q)H(q)e(t),   (7)

where G, H, and F are defined in Equation (6).

Two points about Equation (7) are:

-   1. G is only a function of G₁₁ ^(i), G₁₂ ^(i), G₂₁ ^(i), G₂₂ ^(i),    i=1,2,K.-   2. H is not square.

The first point means that the dynamics of the acoustic path(represented by the acoustic path responses G₁₁ ^(i), G₁₂ ^(i), G₂₁^(i), and G₂₂ ^(i), i<1,2,K) can be identified independently from theexternal signals' e_(i) frequency content (represented by H_(λ) ^(i) andH_(r) ^(i), i=1,2,K).

The second point is an issue in that rectangular noise models may not beidentifiable. In the following text a noise model that is statisticallyequivalent to H in Equation (7) is derived, but it is square. Twostatistically equivalent noise models H₁ and H₂ are such that thestatistics of ν₁ and ν₂ are the same for both noise models (whereν_(i)=H_(i)e, i=1,2, where e_(i) is a white noise process). Inparticular ν₁ and ν₂ are statistically equivalent if they have the samepower spectral density Φ_(v) _(i) =H(e^(jω))H(e^(−jω))σ_(e) ₁ ², whereσ_(e) _(i) ² is the power of the white noise process e_(i)(t).

Noise models are closely related to spectral factors. By the spectralfactorization theorem, any power spectral density matrix Φ(z) can beuniquely factored as Φ(z)=H(z)H(z⁻¹)^(T) where H(z) is a (square) monicstable, minimum phase transfer matrix. For Equation (7) the powerspectral density matrix of the noise is equal to:

$\begin{matrix}{{\Phi_{v}(z)} = {{{H(z)}{H\left( z^{- 1} \right)}^{T}} = \begin{bmatrix}{A_{11}(z)} & {B_{12}(z)} & {C_{13}(z)} & 0 & 0 & 0 \\{B_{21}(z)} & {A_{22}(z)} & {B_{23}(z)} & {C_{24}(z)} & 0 & 0 \\{C_{31}(z)} & {B_{32}(z)} & {A_{33}(z)} & {B_{34}(z)} & {C_{35}(z)} & 0 \\0 & {C_{42}(z)} & {B_{43}(z)} & {A_{44}(z)} & {B_{45}(z)} & {C_{46}(z)} \\0 & 0 & {C_{53}(z)} & {B_{54}(z)} & {A_{55}(z)} & {B_{56}(z)} \\0 & 0 & 0 & {C_{64}(z)} & {B_{65}(z)} & {A_{66}(z)}\end{bmatrix}}} & (8)\end{matrix}$

where

A _(ii)(z)=H _(i,i−1)(z)H _(i,i−1)(z ⁻¹)+H _(ii)(z)H _(ii)(z ⁻¹)+H_(i,i+1)(z)H _(i,i+1)(z ⁻¹)

B _(ij)(z)=H _(ij)(z)H _(jj)(z ⁻¹)+H _(ii)(z)H _(ji)(z ⁻¹)

C _(ij)(z)=H _(i,i−1)(z)H _(j,j−1)(z ⁻¹),

Note that the power spectral density in Equation (8) is 5-diagonalpara-Hermitian matrix. Para-Hermitian means that the (i, j) th entry,Φ_(ij)(z)=Φ_(ji)(z⁻¹). Moreover, no entries in the diagonal bands arezero, as long as there is no situation where C_(ij) or B_(ij) are equalto zero. From Equations (7) and (8):

$C_{ij} = {{{H_{i,{i - 1}}(z)}{H_{j,{j - 1}}\left( z^{- 1} \right)}} = {\frac{{G_{12}^{i - 1}(z)}{N_{i - 1}(z)}{H_{r}^{i - 1}(z)}{G_{21}^{i - 1}\left( z^{- 1} \right)}{N_{j}\left( z^{- 1} \right)}{H_{\lambda}^{j + 1}\left( z^{- 1} \right)}}{{D_{{i - 1},{i - 1}}(z)}{D_{{j - 1},{j - 1}}\left( z^{- 1} \right)}}.}}$

It follows that elements C_(ij) only equal zero if either G₁₂ ^(i−1) orG₂₁ ^(i−1) are zero, which means there is no acoustic energy transferbetween the sensors 116. This, in practice, is unlikely. The sameargument can be made for the elements B_(ij). A 5-diagonal matrix wherenone of the elements in the diagonal bands are zero is hereinafterreferred to as a full 5-diagonal matrix. The following lemma shows thatthe spectral factor of a full 5-diagnal matrix is nearly a full3-diagonal matrix.

Lemma 1: Let Φ_(ν) be an n×n Hermitian matrix. Let H be the unique,monic, stable and minimum phase spectral factor of Φ_(ν). If Φ is a full5-diagonal matrix then H is a full 3-diagonal matrix with possiblynon-zero entries in the (3,1) and (n−2, n) positions and possibly zeroentries in the (2,1) and (n−1, n) positions.

From Equation (8) and Lemma 1 it follows that ν=He can be equivalentlymodelled as ν=

where

is a square, monic, stable, minimum phase full 3-diagonal matrix. Thus,H can be replaced by

in Equation (7) without any changes to w. Consequently, the final modelfor the acoustic sensor setup is:

w(t)=F(q)G(q)F ⁻¹(q)w(t)+F(q)H̆(q)ĕ(t).   (9)

A graphical representation of Equation (9) is shown as a model 400 inFIG. 4. The model 400 depicts measured variables w_(i), i=1,K,6, andexternal sources e_(i), i=1,K,6. The relationship between measurementsw_(i), i=1,2,K and sources

, i=1,2,K can be determined from Equation (9) as

$\begin{matrix}{{w(t)} = {\left( {I - {{F(q)}{G(q)}{F^{- 1}(q)}}} \right)^{- 1}{F(q)}{\overset{\Cup}{H}(q)}{\overset{\Cup}{e}(t)}}} & (10) \\{{= {{F(q)}\left( {I - {G(q)}} \right)^{- 1}{\overset{\Cup}{H}(q)}{\overset{\Cup}{e}(t)}}}{{{Let}\mspace{14mu} {\overset{\Cup}{W}(q)}} = {{F(q)}\left( {I - {G(q)}} \right)^{- 1}{{\overset{\Cup}{H}(q)}.}}}} & (11)\end{matrix}$

Certain points about Equation (9) are summarized in the following list:

-   1. The transfer functions G_(ij), i, j=1,2,K are functions of only    the acoustic path responses, i.e. only G₁₁ ^(i), G₁₂ ^(i), G₂₁ ^(i),    and G₂₂ ^(i), i=1,2,K as defined in Equation (2). Thus a change in    the acoustic path response is reflected by a change in one or more    G_(ij), i, j=1,2,K. In contrast, a change in the loudness or    frequency content of the acoustic sources (external signals e_(i))    does not change any G_(ij), i, j=1,2,K.-   2. A change in the frequency content of the external signals e,    affecting the pipeline 204 results in a change in the acoustic    source transfer functions H_(ij), i, j=1,2,K.-   3. Recall that F is a diagonal matrix of the sensor response    functions. If each sensor has approximately the same response then    F(q)G(q)F⁻¹(q) is approximately independent of the sensor response.    The dominant feature of the sensor response is due to the fact that    each of the sensors 116 is distributed.

Using the first two points it is possible to distinguish between changesin the acoustic path response and changes in the frequency content ofthe external signals e_(i) affecting the pipeline 204.

Implementation

The methods and techniques described above may be implemented using, forexample, Matlab™ software. The method to obtain estimates ofF(q)G(q)F(q) and F(q)

(q) in Equation (9) is split into three actions. In the first action theprocessor 102 estimates the matrix

in Equation (10) from the data. In the second action the processor 102factors the estimated

into F(q)G(q)F⁻¹(q) and F(q)

(q) as defined in Equation (9). In the last action the processor 102further refines the estimates of F(q)G(q)F⁻¹(q) and F(q)

(q) to reduce prediction error.

The method for the first action, i.e. estimating

in Equation (9) from data, is a by-product of estimating the sourcepowers using, for example, a technique such as that presented in chapter6 of Huang, Y., Benesty, J., and Chen, J. (2006), Acoustic MIMO SignalProcessing, Signals and Communication Technology, Springer-Verlag BerlinHeidelberg and in chapter 7 of Liung, L. (1999), System Identification,Theory for the User, 2^(nd) Edition, Prentice Hall, the entireties ofboth of which are hereby incorporated by reference. In this action, theprocessor 102 determines an estimate of

, where each element of

(q, θ) is a parameterized transfer function that is parameterized usinga Finite Impulse Response (FIR) structure, i.e. the elements areparameterized as:

W _(ij)(q,θ)=θ_(ij) ⁽¹⁾ q ^(−d) ^(ij) +θ_(ij) ⁽²⁾ q ^(−d) ^(ij)⁻¹+Λ+θ_(ij) ^((m)) q ^(−d) ^(ij) ^(−m) , i, j=1,2,K, i≠j,

W _(ii)(q,θ)=1+θ_(ii) ⁽¹⁾ q ⁻¹+Λ+θ_(ii) ^((m)) q ^(−m) , i=1,2,K,

where d_(ij) is the delay is the delay of the (i,j)th off-diagonaltransfer function representing the time it takes for an acoustic wave totravel between the sensors 116 and θ_(ij) is a parameter to beestimated.

When performing the second action, the processor 102 factors theestimate

(q,{circumflex over (θ)}) into G and H, where {circumflex over (θ)} isan estimated version of θ. The processor 102 in one example embodimentdoes this factorization using a linear regression. It is desirable tofactor

as:

W̆(q,θ)=B ⁻¹(q,β)A(q,α),   (12)

where α and β are parameter vectors that define A and B. From Equation(9), A(q, α) is an estimate of F(q)

(q), and B(q, β) is an estimate of F(q)(I−G(q))⁻¹F⁻¹(q). In addition,from Equation (9) the matrices F(q)

(q) and F(q)(I−G(q))⁻¹F⁻¹(q) have a particular structure. Therefore, Aand B are parameterized with the same matrix structure:

${{A\left( {q,\alpha} \right)} = \begin{bmatrix}1 & {A_{12}\left( {q,\alpha} \right)} & \; & \; & \; \\{A_{21}\left( {q,\alpha} \right)} & 1 & {A_{23}\left( {q,\alpha} \right)} & \; & \; \\\; & {A_{32}\left( {q,\alpha} \right)} & O & O & \; \\\; & \; & O & 1 & {A_{{L - 1},L}\left( {q,\alpha} \right)} \\\; & \; & \; & {A_{L,{L - 1}}\left( {q,\alpha} \right)} & 1\end{bmatrix}},{{B\left( {q,\beta} \right)} = \begin{bmatrix}{B_{11}\left( {q,\beta} \right)} & {B_{12}\left( {q,\beta} \right)} & \; & \; & \; \\{B_{21}\left( {q,\beta} \right)} & {B_{22}\left( {q,\beta} \right)} & {B_{23}\left( {q,\beta} \right)} & \; & \; \\\; & {B_{32}\left( {q,\beta} \right)} & O & O & \; \\\; & \; & O & {B_{{L - 1},{L - 1}}\left( {q,\beta} \right)} & {B_{{L - 1},L}\left( {q,\beta} \right)} \\\; & \; & \; & {B_{L,{L - 1}}\left( {q,\beta} \right)} & {B_{LL}\left( {q,\beta} \right)}\end{bmatrix}},$

where each A_(ij)(q, α), and B_(ij)(q, β) are parameterized transferfunctions. Each A_(ij)(q, α), and B_(ij)(q, β) are parameterized using aFIR structure, although in different embodiments (not depicted) adifferent parameterization may be used. This choice ensures uniquenessof the estimates and also makes the estimation of α and β easier. Inparticular the processor 102 parameterizes A_(ij)(q, α), and B_(ij)(q,β) as

A _(ij)(q, α)=α_(ij) ⁽¹⁾ q ^(−d) ^(ij) +α_(ij) ⁽²⁾ q ^(−d) ^(ij)⁻¹+Λ+α_(ij) ^((m)) q ^(−d) ^(ij) ^(−m) , i, j=1,2,K,

B _(ij)(q, β)=β_(ij) ⁽¹⁾ q ^(d) ^(ij) +β_(ij) ⁽²⁾ q ^(d) ^(ij)⁻¹+Λ+β_(ij) ^((m)) q ^(−d) ^(ij) ^(−m) , i,j=1,2,K, i≠j,

B _(ii)(q, β)=1+β_(ii) ⁽¹⁾ q ⁻¹+Λ+β_(ii) ^((m)) q ^(−m) , i=1,2,K.

The parameterization is entirely defined by α, β, d_(ij), i, j=1,2,K,and m.

From Equation (12) it follows that

B(q, β)W (q, {circumflex over (θ)})=A(q, α).   (13)

Because W, A, and B are parameterized using an FIR structure, α and βappear linearly in Equation (13). This means that the equations can bere-organized to gather all elements of α and β into a vector:

${{\begin{bmatrix}P & {M\left( \hat{\theta} \right)}\end{bmatrix}\begin{bmatrix}\alpha \\\beta\end{bmatrix}} = {\zeta \left( \hat{\theta} \right)}},$

where ζ({circumflex over (θ)}) is a vector. Due to the structure of Aand B because W and B are parameterized with monic transfer functions onthe diagonal, it follows that [P M ({circumflex over (θ)})] is squareand always full rank. Therefore, estimates of α and β can be obtainedas:

$\begin{matrix}{\begin{bmatrix}\hat{\alpha} \\\hat{\beta}\end{bmatrix} = {\begin{bmatrix}P & {M\left( \hat{\theta} \right)}\end{bmatrix}^{- 1}{{\zeta \left( \hat{\theta} \right)}.}}} & (14)\end{matrix}$

In certain embodiments the processor 102 uses any one or more of severalmethods to further refine {circumflex over (α)} and {circumflex over(β)} such that they better represent the data. For example, theprocessor 102 may use a Weighted Null Space Least Squares (WNLS) method.The processor 102 may use WNLS to iteratively minimize the predictionerror by iteratively adjusting the value of {circumflex over (θ)}.

For example, in certain example embodiments the processor 102iteratively selects values of {circumflex over (θ)} until the predictionerror converges such that a stopping criterion is satisfied. Inembodiments in which the processor 102 selects {circumflex over (θ)}using Equation (21), for example, the processor 102 may iterativelyselect {circumflex over (θ)} until the difference between successiveiterations is small enough to satisfy the stopping criterion. In onespecific example, the processor 102 ceases iterating when successiveiterations of the slope of the objective function being minimized issmall enough (e.g., a difference of less than 1×10⁻⁴) to satisfy thestopping criterion.

The processor 102 also determines when an estimated acoustic pathresponse and/or an acoustic source transfer function has changed. Inorder to continuously monitor the pipeline 204, the processor 102segments the data coming collected using the fiber 112 into blocks of acertain duration, each of which in the depicted embodiment is one minutelong. For each block of data, the processor 102 determines estimates ofF(q)G(q)F⁻¹(q) and F(q)

(q).

The result is that the processor 102 determines a sequence of estimatedtransfer functions in the form of the acoustic path responses and theacoustic source transfer functions. The processor 102 then monitors theestimated transfer functions for changes. Depending on which transferfunction changes, the change may represent a change in the acoustic path(e.g., a hole in the pipeline 204) or a change in the frequency contentof the external sources e, (e.g., a truck driving in the vicinity of thepipeline 204). Because the processor 102 compares two estimated transferfunctions, in certain embodiments the processor 102 determines theconfidence bounds for each transfer function. The processor 102 thenuses the confidence bounds to determine the statistical distance betweenthe two estimated frequency response functions at a particularfrequency. The processor 102 does this as follows.

Let G(e^(jω), {circumflex over (θ)}) and

(e^(jω), {circumflex over (θ)}) denote the frequency response functionsof the estimates of G and

. The covariance of the frequency response functions of the estimatedtransfer functions is

${{{Cov}\begin{bmatrix}{G\left( {e^{j\; \omega},\hat{\theta}} \right)} \\{\overset{(}{H}\left( {e^{j\; \omega},\hat{\theta}} \right)}\end{bmatrix}} \approx {\frac{1}{N}{T\left( {e^{j\; \omega},\theta_{0}} \right)}P_{\theta}{T\left( {e^{{- j}\; \omega},\theta_{0}} \right)}}},$

where

${{T\left( {e^{j\; \omega},\theta} \right)} = \begin{bmatrix}{\frac{d}{d\; \theta}{G\left( {e^{j\; \omega},\theta} \right)}} & {\frac{d}{d\; \theta}{\overset{(}{H}\left( {e^{j\; \omega},\hat{\theta}} \right)}}\end{bmatrix}},$

and P_(θ) is the covariance matrix of the estimated parameter vector:

P ₇₄ =(Ē[ψ(t,θ ₀)Λ₀ ¹ψ^(T)(t,θ ₀)])⁻¹,

where

${{\psi \left( {t,\theta} \right)} = {{- \frac{d}{d\; \theta}}{ɛ\left( {t,\theta} \right)}}},$

where ε is the prediction error.

Let the variance of G(e^(jω), {circumflex over (θ)}) and H(e^(jω),{circumflex over (θ)}) be denoted σ_(G) ²(e^(jω)) and σ_(H) ²(e^(jω))respectively. Then the statistical difference between two estimatesG(e^(jω), {circumflex over (θ)}₁) and G(e^(jω), {circumflex over (θ)}₂)is:

$\begin{matrix}{{d\left( e^{j\; \omega} \right)} = {\sqrt{2}\frac{{G\left( {e^{j\; \omega},{\hat{\theta}}_{1}} \right)} - {G\left( {e^{j\; \omega},{\hat{\theta}}_{2}} \right)}}{\sqrt{{\sigma_{G}^{2}\left( {e^{j\; \omega},\theta_{1}} \right)} - {\sigma_{G}^{2}\left( {e^{j\; \omega},\theta_{2}} \right)}}}}} & (15)\end{matrix}$

The processor 102 determines the statistical distance at each frequencyof the frequency response functions. From Equation (15) it follows thatif the estimates G(e^(jω), {circumflex over (θ)}₁) and G(e^(jω),{circumflex over (θ)}₂) are very different at frequencies where thevariance of the estimates are small, then the statistical distancebetween them is large. In contrast, if the estimates G(e^(jω),{circumflex over (θ)}₁) and G(e^(jω), {circumflex over (θ)}₂) are verydifferent at frequencies where the variance of the estimates is large,then the statistical distance between the estimates is not as big asbefore. Thus, by using statistical difference to monitor for changes intransfer functions, the processor 102 incorporates uncertaintyassociated with the estimates into the monitoring method.

Accordingly, in one embodiment consistent with the above description,the method for detecting whether the acoustic event has occurredcomprises, given periodically refreshed data sets of length N obtainedfrom L channels of the sensor as shown in FIG. 2:

-   1. Choose parameterization for the matrices W (q, θ), A(q, αa) and    B(q, β).-   2. For each new data set that is received, the processor 102:    -   (a) Estimates        in Equation (9) by estimating source powers.    -   (b) Using        ({circumflex over (θ)}), determines estimates of F(q)G(q)F⁻¹(q)        and F(q)        (q), as outlined in Equations (12) to (14).    -   (c) Refines the estimates of F(q)G(q)F⁻¹(q) and F(q)        (q) using WNLS.    -   (d) Determines the variance of the frequency response functions        of the estimated transfer functions.-   3. Determine the statistical distance to the previous estimates    using Equation (15).

One example embodiment of this method is depicted in FIG. 10, which maybe expressed as computer program code and performed by the processor102. In FIG. 10, the processor 102 begins at block 1002 and proceeds toblock 1004 where it determines a linear relationship between themeasured acoustic signal and the white noise acoustic source (externalsource e_(i)) located along a longitudinal segment of the fluid conduitoverlapping the sensor. The processor 102 then proceeds to block 1006where, from the linear relationship, it determines an acoustic pathresponse and an acoustic source transfer function that transforms thewhite noise acoustic source. In one embodiment the processor 102 doesthis by determining F(q)G(q)F⁻¹(q) and F(q)

(q) as described above. Determining F(q)G(q)F⁻¹(q) and F(q)

(q) for a portion of the fiber 112 results in determining the acousticpath response and acoustic source transfer function for each of thesensors 116 comprising that portion of the fiber 112. The processor 102performs blocks 1004 and 1006 for all of the sensors 116.

The processor 102 then proceeds to block 1008 where it monitors overtime variations in one or both of the acoustic path responses andacoustic source transfer functions. An example of this is determiningstatistical differences of one or both of the acoustic path responsesand acoustic source transfer functions as described above.

The processor 102 subsequently proceeds to block 1010 where itdetermines whether at least one of the variations exceeds an eventthreshold. An example of this is determining whether the determinedstatistical differences exceed the event threshold.

If not, the processor 102 proceeds to block 1014 and the method of FIG.10 ends.

If at least one of the power estimates exceeds the event threshold, theprocessor 102 proceeds from block 1010 to 1012. At block 1012, theprocessor 102 attributes the acoustic event 208 to one of the sensors116 for which the acoustic path response or acoustic source transferfunction varied in excess of the event threshold. For example, theprocessor 102 may attribute the acoustic event 208 to the one of thesensors 116 for which the acoustic path response or acoustic sourcetransfer function most exceeds the event threshold. Alternatively, inembodiments in which there are multiple acoustic events, the processor102 may attribute one of the acoustic events 208 to each of the sensors116 for which the acoustic path response or acoustic source transferfunction exceeds the event threshold. In one example embodiment in whichthere is only one acoustic event 208, the event threshold is selectedsuch that the acoustic path response or acoustic source transferfunction exceeds the event threshold for only one of the sensors 116,and the acoustic event 208 is attributed to that sensor 116.

In embodiments in which there are multiple acoustic events 208, thepower estimates of the acoustic sources attributed to multiple of thesensors 116 may exceed the event threshold; in the current embodiment,the processor 102 attributes a different acoustic event 208 to each ofthe sensors 116 i to which is attributed an acoustic source that exceedsthe event threshold. The event threshold for the sensors 116 may beidentical in certain embodiments; in other embodiments, the eventthresholds may differ for any two or more of the sensors 116.

In embodiments in which the acoustic event 208 is the leak, theprocessor 102 determines the acoustic event as affecting thelongitudinal segment of the pipeline 204 corresponding to the sensor 116to which the acoustic event is attributed.

In at least some example embodiments, a test signal may be generated andused to do one or both of generate and test the acoustic path responsesand the acoustic source transfer functions. The test signal may, forexample, be an impulse signal, or white noise comprising a wide acousticband, a frequency sweep signal, or pings of various frequencies. Using aknown acoustic input allows better estimation of the acoustic pathresponse and the acoustic source transfer functions because it reducesthe uncertainty regarding the input signals and improves the transferfunction calculations based on the relationship between the measuredoutput and the known input signals. In embodiments in which the inputsignal is or approximates an ideal impulse signal, the frequency domainconversion of the measured output signal is or approximates the acousticpath response.

EXAMPLES

FIG. 5 depicts test equipment used to validate the method describedabove, while FIGS. 6-8 depict the associated experimental results. Moreparticularly, FIG. 5 depicts equipment 500 comprising a rectangularpiece of acoustic foam 502 laid on the floor 503 of a room. Outside ofthe foam 502 and adjacent the centers of the foam's 502 short sides aretwo pieces of PVC pipe around which the optical fiber 112 and FBGs 114are wrapped, and which consequently act as the sensors 116. A firstspeaker 504 a and a second speaker 504 b are adjacent the PVC pipe (thespeakers 504 a,b are collectively “speakers”).

Two uncorrelated sequences of Gaussian noise were generated. Each signalwas split into 4 parts. Parts 1-4 were filtered by a Chebyshev Type 1Bandpass filter of order 2, 3, 4, and 5, respectively. The signals wereplayed over the speakers 504 a,b. The ordering of the first signal wasr₁, r₂, r₃, r₄, and r₁, where r_(i) denotes the signal filtered withbandpass filter i. The transition times of the signals are t=6, 30, 54,78 mins. The ordering of the second signal is r₃, r₄, r₁, r₂, and r₃. Inaddition, the second signal is shifted such that the transition betweenfilters occur at t=18, 42, 66, 90 mins. Therefore, at all times, bothspeakers 504 are playing sequences with different spectral content, andat no time are both speakers 504 changing their spectral contentsimultaneously. The speakers 504 are the external signals e_(i), and thefrequency content of the external signals e_(i) is the frequency contentof the signals played over the speakers 504. A spectrogram of thefrequency content of both speakers 504 in shown in the upper two plotsof FIG. 6.

The acoustic path in FIG. 5 is the air and the physics of the roomcontaining the foam 502. During the experiment a foam block (notdepicted) was placed in the room at time t=12 mins and then it wasremoved again at time t=36 mins. A plastic case (not depicted) wasplaced in the room in between the speakers 504 at time t=60 mins andremoved at time t=85 mins. Placing objects in the room is a way to alterthe acoustic path between the two sensors. Background noise was presentduring the collection of the data including noise from heaters, lights,outside traffic, talking in adjacent rooms, etc. The objective of theexperiment was to be able to determine when the first speaker 504 achanged its frequency content, when the second speaker 504 b changed itsfrequency content, and finally when the acoustic path response changed,given only data obtained from the fiber optic sensors in the room. Thebottom two plots of FIG. 6 show a spectrogram of the measured acousticsignals. As can be seen the measured signals change at many times, andit is not clear what has changed when only visually inspecting themeasured signals' spectra.

In FIG. 7 the estimated acoustic path response is shown over theduration of the experiment. The changes at times t=24, 72, 120, 170 arevery noticeable. Furthermore, the estimates appear relatively constantduring the time between those changes.

In FIG. 8 the estimated frequency content of the external signals e, isplotted. Again, the changes in the signals correspond with the changesin the source, and during the times that there are no changes, theestimates appear relatively constant. FIG. 8 shows the estimatedexternal signal frequency content does change when the acoustic channelis changed (by placing objects in the room). This is as expected byEquation (9), which shows that the estimated transfer function matrixF(q)

(q) is a function of the acoustic path response G₁₁ ^(i), G₁₂ ^(i), G₂₁^(i), and G₂₂ ^(i), i=1,2.

In FIG. 9 the processor 102 determines the statistical difference forthe current estimate of the acoustic path response relative to theestimate 5 time blocks ago. If the acoustic path changes, and remainsconstant for at least 5 time blocks, the processor 102 depicts this as adark vertical line having a width of 5 time blocks in the plot. The widevertical lines in the plot accordingly match the times when the acousticpath was changed. In addition there do not appear to be any othervertical lines in the plot, which means that the acoustic channel wasconstant between the changes. By comparing FIGS. 6 and 9 it appears thatthe statistical difference provides a clearer indication of when theacoustic path significantly changed.

In FIG. 9 the processor 102 determines the statistical difference forthe current estimate of the frequency content of the external signals tothe estimate 5 time blocks ago. If the frequency content of the externalsignals changes, and remains constant for at least 5 time blocks, theprocessor 102 displays this as a dark vertical line of width 5 timeblocks in the plot. This is the case when the speakers 504 a,b changetheir frequency content. On the other hand if the frequency content ofthe external signals e, changes only for a short time (<1 time block),this shows up as 2 vertical lines of width 1 time block each, spaced 5time blocks apart. This is the case when a person walked into the roomto place or remove an object.

The embodiments have been described above with reference to flowchartsand block diagrams of methods, apparatuses, systems, and computerprogram products. In this regard, the flowchart and block diagram inFIGS. 1A, 3, 4, and 10 illustrate the architecture, functionality, andoperation of possible implementations of various embodiments. Forinstance, each block of the flowcharts and block diagrams may representa module, segment, or portion of code, which comprises one or moreexecutable instructions for implementing the specified logicalfunction(s). In some different embodiments, the functions noted in thatblock may occur out of the order noted in those figures. For example,two blocks shown in succession may, in some embodiments, be executedsubstantially concurrently, or the blocks may sometimes be executed inthe reverse order, depending upon the functionality involved. Somespecific examples of the foregoing have been noted above but those notedexamples are not necessarily the only examples. Each block of the blockdiagrams and flowcharts, and combinations of those blocks, may beimplemented by special purpose hardware-based systems that perform thespecified functions or acts, or combinations of special purpose hardwareand computer instructions.

Each block of the flowcharts and block diagrams and combinations thereofcan be implemented by computer program instructions. These computerprogram instructions may be provided to a processor of a general purposecomputer, special purpose computer, or other programmable dataprocessing apparatus to produce a machine, such that the instructions,which execute via the processor of the computer or other programmabledata processing apparatus, create means for implementing the functionsor acts specified in the blocks of the flowcharts and block diagrams.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions thatimplement the function or act specified in the blocks of the flowchartsand block diagrams. The computer program instructions may also be loadedonto a computer, other programmable data processing apparatus, or otherdevices to cause a series of operational steps to be performed on thecomputer, other programmable apparatus or other devices to produce acomputer implemented process such that the instructions that execute onthe computer or other programmable apparatus provide processes forimplementing the functions or acts specified in the blocks of theflowcharts and block diagrams.

As will be appreciated by one skilled in the art, embodiments of thetechnology described herein may be embodied as a system, method, orcomputer program product. Accordingly, these embodiments may take theform of an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware that may all generally bereferred to herein as a “circuit,” “module,” or “system.” Furthermore,embodiments of the presently described technology may take the form of acomputer program product embodied in one or more non-transitory computerreadable media having stored or encoded thereon computer readableprogram code.

Where aspects of the technology described herein are implemented as acomputer program product, any combination of one or more computerreadable media may be utilized. A computer readable medium may comprisea computer readable signal medium or a non-transitory computer readablemedium used for storage. A non-transitory computer readable medium maycomprise, for example, an electronic, magnetic, optical,electromagnetic, infrared, or semiconductor system, apparatus, ordevice, or any suitable combination thereof. Additional examples ofnon-transitory computer readable media comprise a portable computerdiskette, a hard disk, RAM, ROM, an erasable programmable read-onlymemory (EPROM or flash memory), a portable compact disc read-only memory(CD-ROM), an optical storage device, a magnetic storage device, or anysuitable combination thereof. As used herein, a non-transitory computerreadable medium may comprise any tangible medium that can contain,store, or have encoded thereon a program for use by or in connectionwith an instruction execution system, apparatus, or device. Thus,computer readable program code for implementing aspects of theembodiments described herein may be contained, stored, or encoded on thecomputer readable medium 104 of the signal processing device 118.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, radiofrequency, and the like, or anysuitable combination thereof. Computer program code for carrying outoperations comprising part of the embodiments described herein may bewritten in any combination of one or more programming languages,including an object oriented programming language and proceduralprogramming languages. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer or server. In the latterscenario, the remote computer may be connected to the user's computerthrough any type of network, including a local area network (LAN) or awide area network (WAN), or the connection may be made to an externalcomputer (e.g., through the Internet using an Internet ServiceProvider).

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting. Accordingly, asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises” and“comprising,” when used in this specification, specify the presence ofone or more stated features, integers, steps, operations, elements, andcomponents, but do not preclude the presence or addition of one or moreother features, integers, steps, operations, elements, components, andgroups. Directional terms such as “top”, “bottom”, “upwards”,“downwards”, “vertically”, and “laterally” are used in the followingdescription for the purpose of providing relative reference only, andare not intended to suggest any limitations on how any article is to bepositioned during use, or to be mounted in an assembly or relative to anenvironment. Additionally, the term “couple” and variants of it such as“coupled”, “couples”, and “coupling” as used in this description areintended to include indirect and direct connections unless otherwiseindicated. For example, if a first device is coupled to a second device,that coupling may be through a direct connection or through an indirectconnection via other devices and connections. Similarly, if the firstdevice is communicatively coupled to the second device, communicationmay be through a direct connection or through an indirect connection viaother devices and connections.

One or more example embodiments have been described by way ofillustration only. This description is been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the form disclosed. Many modifications and variations will beapparent to those of ordinary skill in the art without departing fromthe scope of the claims. It will be apparent to persons skilled in theart that a number of variations and modifications can be made withoutdeparting from the scope of the claims. In construing the claims, it isto be understood that the use of a computer to implement the embodimentsdescribed herein is essential at least where the presence or use ofcomputer equipment is positively recited in the claims.

1. A method for determining whether an acoustic event has occurred alonga fluid conduit having acoustic sensors positioned therealong, themethod comprising: (a) determining, using a processor and for each ofthe sensors: (i) a linear relationship between a measured acousticsignal measured using the sensor and a white noise acoustic sourcelocated along a longitudinal segment of the fluid conduit overlappingthe sensor; and (ii) from the linear relationship, an acoustic pathresponse and an acoustic source transfer function that transforms thewhite noise acoustic source; (b) monitoring over time variations in oneor both of the acoustic path responses and acoustic source transferfunctions; (c) determining whether at least one of the variationsexceeds an event threshold; and (d) when at least one of the variationsexceeds the event threshold, attributing the acoustic event to one ofthe sensors corresponding to the acoustic path response or acousticsource transfer function that varied in excess of the event threshold.2. The method of claim 1 wherein the processor attributes the acousticevent to the one of the sensors for which the variation most exceeds theevent threshold.
 3. The method of claim 1 wherein the acoustic eventcomprises one of multiple acoustic events, and wherein the processorattributes one of the acoustic events to each of the sensors for whichthe variation exceeds the event threshold.
 4. The method of claim 1,wherein the acoustic path response comprises an acoustic response of thelongitudinal segment and the acoustic event is identified as havingoccurred along the longitudinal segment corresponding to the sensor towhich the acoustic event is attributed.
 5. The method of claim 4wherein, for each of the channels, the processor determines the linearrelationship between the measured acoustic signal, the white noiseacoustic source located along the longitudinal segment, and white noiseacoustic sources located along any immediately adjacent longitudinalsegments.
 6. The method of claim 4 wherein each element of the linearrelationship is a parameterized transfer function that is parameterizedusing a finite impulse response structure.
 7. The method of claim 4wherein the processor determines the acoustic path responses andacoustic source transfer functions by factoring the linear relationshipusing a linear regression, wherein the linear regression is factoredinto a first array of parameterized transfer functions for determiningthe acoustic path responses and a second array of parameterized transferfunctions for determining the acoustic source transfer functions.
 8. Themethod of claim 7 wherein each of the first and second arrays isparameterized using a finite impulse response structure.
 9. The methodof to claim 4 further comprising, prior to monitoring variations in oneor both of the acoustic path responses and acoustic source transferfunctions, refining the one or both of the acoustic path responses andacoustic source transfer functions using weighted nullspace leastsquares.
 10. The method of claim 4 wherein (b)-(d) comprise: (a)determining a confidence bound for each of: (i) two of the acoustic pathresponses; or (ii) two of the acoustic source transfer functions; (b)from the confidence bounds, determining a statistical distance betweenthe two of the acoustic source responses or the two of the acousticsource transfer functions; (c) comparing the statistical distance to theevent threshold; and (d) identifying the acoustic event as havingoccurred when the statistical distance exceeds the event threshold. 11.The method of claim 4 further comprising dividing the measured acousticsignal into blocks of a certain duration prior to determining the linearrelationship.
 12. The method of claim 4 wherein each of the longitudinalsegments is delineated by a pair of fiber Bragg gratings located alongan optical fiber and tuned to substantially identical centerwavelengths, and further comprising optically interrogating the opticalfiber in order to obtain the measured acoustic signal.
 13. The method ofclaim 12 wherein the optical fiber extends parallel to the fluidconduit.
 14. The method of claim 12 wherein the optical fiber is wrappedaround the fluid conduit.
 15. The method of claim 13 wherein the opticalfiber is within a fiber conduit laid adjacent the fluid conduit.
 16. Themethod of claim 4 wherein the fluid conduit comprises a pipeline.
 17. Asystem for detecting whether an acoustic event has occurred along afluid conduit longitudinally divided into measurements channels, thesystem comprising: (a) an optical fiber extending along the conduit andcomprising fiber Bragg gratings (FBGs), wherein each of the measurementchannels is delineated by a pair of the FBGs tuned to substantiallyidentical center wavelengths; (b) an optical interrogator opticallycoupled to the optical fiber and configured to optically interrogate theFBGs and to output an electrical measured acoustic signal; and (c) asignal processing unit comprising: (i) a processor communicativelycoupled to the optical interrogator; and (ii) a non-transitory computerreadable medium communicatively coupled to the processor, wherein themedium has computer program code stored thereon that is executable bythe procssor and that, when executed by the processor, causes theprocessor to perform the method of claim
 1. 18. The system of claim 17wherein the optical fiber extends parallel to the fluid conduit.
 19. Thesystem of claim 17 wherein the optical fiber is wrapped around the fluidconduit.
 20. The system of claim 17 further comprising a fiber conduitadjacent the fluid conduit, wherein the optical fiber extends within thefiber conduit.
 21. The system of claim 17 wherein the fluid conduitcomprises a pipeline.
 22. A non-transitory computer readable mediumhaving stored thereon computer program code that is executable by aprocessor and that, when executed by the processor, causes the processorto perform the method of claim 1.